This paper deals with the control of fixed bed bioreactors. The dynamics of these processes are described by a nonlinear distributed parameter model. In a first step, the partial differential equations of the model are reduced to ordinary differential equations by using an orthogonal collocation method. A nonlinear adpative controller is then designed, which is based on the nonlinear discretized model. Its performance is illustrated by simulation results on a fixed bed anaerobic waste water treatment process.
Dochain, D., Babary, J. P., & Tall-Maamar, N. (1992). Modeling and Adaptive-control of Nonlinear Distributed Parameter Bioreactors Via Orthogonal Collocation. Automatica, 28(5), 873-883. https://doi.org/10.1016/0005-1098(92)90141-2 (Original work published 1992)